I think one important thing to add to Arno's answer is that while there is no direct impact on the PIs salary, there (at least in theory) should be one on their workload. A typical research-oriented Lecturer/Senior Lecturer in the UK is supposed to spend 40% of their time on research, 40% on teaching-related activities, and 20% on admin. In a way, teaching-and-admin duties an academic performs "pay" for their allotted research time.
If that academic then gets a research grant on which they are costed to work for 40% FTE (which covers 40% of their salary), this does not mean they should spend all their research time on this project. In fact, these 40% should be taken out of their overall workload, and ideally out of their teaching+admin workload. This is sometimes referred to as buying out your teaching time.
So in principle, the academic from the above paragraph would go from 40(R)-40(T)-20(A) workload to 100(R) workload (ideally), or at least to a 64(R)+24(T)+12(A) (in case 40% of their combined R-T-A workload gets assigned to research on this new project). The grant money, which goes to the institution, should be used to cover the reduction in the PIs teaching workload (e.g. to hire somebody on a fixed-term teaching-only position).
As mentioned in the previous answers, successfully securing external funding is one of the conditions for promotions as well.